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Consider a uniprocessor system executing three tasks T1, T2 and T3, each of which is composed of an infinite sequence of jobs (or instances) which arrive periodically at intervals of 3, 7 and 20 milliseconds, respectively. The priority of each task is the inverse of its period and the available tasks are scheduled in order of priority, with the highest priority task scheduled first. Each instance of T1, T2 and T3 requires an execution time of 1, 2 and 4 milliseconds, respectively. Given that all tasks initially arrive at the beginning of the 1st milliseconds and task preemptions are allowed, the first instance of T3 completes its execution at the end of ______________ milliseconds.
  • a)
    5
  • b)
    10
  • c)
    12
  • d)
    15
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
Consider a uniprocessor system executing three tasks T1, T2 and T3, ea...
Periods of T1, T2 and T3 are 3ms, 7ms and 20ms. Since priority is inverse of period, T1 is the highest priority task, then T2 and finally T3 Every instance of T1 requires 1ms, that of T2 requires 2ms and that of T3 requires 4ms Initially all T1, T2 and T3 are ready to get processor, T1 is preferred Second instances of T1, T2, and T3 shall arrive at 3, 7, and 20 respectively. Third instance of T1, T2 and T3 shall arrive at 6, 14, and 40 respectively.
Time-Interval  Tasks   
 0-1            T1     
 1-2            T2      
 2-3            T2     
 3-4            T1  [Second Instance of T1 arrives] 
 4-5            T3     
 5-6            T3     
 6-7            T1  [Third Instance of T1 arrives]  
                     [Therefore T3 is preempted] 
 7-8            T2  [Second instance of T2 arrives]                            
 8-9            T2
 9-10          T1  [Fourth Instance of T1 arrives]
 10-11        T3
11-12         T3 [First Instance of T3 completed]
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Most Upvoted Answer
Consider a uniprocessor system executing three tasks T1, T2 and T3, ea...
Periods of T1, T2 and T3 are 3ms, 7ms and 20ms. Since priority is inverse of period, T1 is the highest priority task, then T2 and finally T3 Every instance of T1 requires 1ms, that of T2 requires 2ms and that of T3 requires 4ms Initially all T1, T2 and T3 are ready to get processor, T1 is preferred Second instances of T1, T2, and T3 shall arrive at 3, 7, and 20 respectively. Third instance of T1, T2 and T3 shall arrive at 6, 14, and 40 respectively.
Time-Interval  Tasks   
 0-1            T1     
 1-2            T2      
 2-3            T2     
 3-4            T1  [Second Instance of T1 arrives] 
 4-5            T3     
 5-6            T3     
 6-7            T1  [Third Instance of T1 arrives]  
                     [Therefore T3 is preempted] 
 7-8            T2  [Second instance of T2 arrives]                            
 8-9            T2
 9-10          T1  [Fourth Instance of T1 arrives]
 10-11        T3
11-12         T3 [First Instance of T3 completed]
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Community Answer
Consider a uniprocessor system executing three tasks T1, T2 and T3, ea...
To solve this problem, we need to determine the completion time of the first instance of task T3.

Step 1: Calculating the priority of each task
The priority of each task is defined as the inverse of its period. So, we can calculate the priority of each task as follows:
- Task T1: 1/3 = 0.33
- Task T2: 1/7 = 0.14
- Task T3: 1/20 = 0.05

Step 2: Scheduling the tasks
The tasks are scheduled in order of priority, with the highest priority task scheduled first. Since preemptions are allowed, the tasks will be scheduled as follows:
- At time 0 milliseconds, task T1 is scheduled.
- At time 3 milliseconds, task T1 completes its execution and task T2 is scheduled.
- At time 5 milliseconds, task T3 arrives, but since task T2 has higher priority, it continues executing.
- At time 7 milliseconds, task T2 completes its execution and task T3 is scheduled.
- At time 9 milliseconds, task T3 is preempted by the arrival of task T1.
- At time 12 milliseconds, task T1 completes its execution and task T3 resumes execution.
- At time 16 milliseconds, task T3 is preempted by the arrival of task T2.
- At time 19 milliseconds, task T2 completes its execution and task T3 resumes execution.
- At time 23 milliseconds, task T3 completes its execution.

Step 3: Finding the completion time of the first instance of task T3
Since the first instance of task T3 completes its execution at time 23 milliseconds, the correct answer is option 'C' - 12 milliseconds.
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Consider a uniprocessor system executing three tasks T1, T2 and T3, each of which is composed of an infinite sequence of jobs (or instances) which arrive periodically at intervals of 3, 7 and 20 milliseconds, respectively. The priority of each task is the inverse of its period and the available tasks are scheduled in order of priority, with the highest priority task scheduled first. Each instance of T1, T2 and T3 requires an execution time of 1, 2 and 4 milliseconds, respectively. Given that all tasks initially arrive at the beginning of the 1st milliseconds and task preemptions are allowed, the first instance of T3 completes its execution at the end of ______________ milliseconds.a)5b)10c)12d)15Correct answer is option 'C'. Can you explain this answer?
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